Exercise 42 Page 279

We want to find the domain and range of the exponential function shown in the given diagram.

Let's analyze the function. y=- (0.5)^x-1 ⇓ y=- 1(0.5)^x- 1 Looking at the function, we can see that its parent function y=(0.5)^x has been reflected across the x-axis and translated 1 unit down. Therefore, the asymptote of the function is the line y=- 1.

The domain of the function is all real numbers. The function cannot be greater than - 1, so the range of the function is all real numbers less than - 1, not 0. Domain:& - ∞ < x < ∞ Range:& y < - 1